An iterated loop matching approach to the prediction of RNA secondary structures with pseudoknots

MOTIVATION: Pseudoknots have generally been excluded from the prediction of RNA secondary structures due to its difficulty in modeling. Although, several dynamic programming algorithms exist for the prediction of pseudoknots using thermodynamic approaches, they are neither reliable nor efficient. On the other hand, comparative methods are more reliable, but are often done in an ad hoc manner and require expert intervention. Maximum weighted matching, an algorithm for pseudoknot prediction with comparative analysis, suffers from low-prediction accuracy in many cases. RESULTS: Here we present an algorithm, iterated loop matching, for reliably and efficiently predicting RNA secondary structures including pseudoknots. The method can utilize either thermodynamic or comparative information or both, thus is able to predict pseudoknots for both aligned and individual sequences. We have tested the algorithm on a number of RNA families. Using 8-12 homologous sequences, the algorithm correctly identifies more than 90% of base-pairs for short sequences and 80% overall. It correctly predicts nearly all pseudoknots and produces very few spurious base-pairs for sequences without pseudoknots. Comparisons show that our algorithm is both more sensitive and more specific than the maximum weighted matching method. In addition, our algorithm has high-prediction accuracy on individual sequences, comparable with the PKNOTS algorithm, while using much less computational resources. AVAILABILITY: The program has been implemented in ANSI C and is freely available for academic use at http://www.cse.wustl.edu/~zhang/projects/rna/ilm/ Supplementary information: http://www.cse.wustl.edu/~zhang/projects/rna/ilm/     

Biphasic folding kinetics of RNA pseudoknots and telomerase RNA activity

Using a combined master equation and kinetic cluster approach, we investigate RNA pseudoknot folding and unfolding kinetics. The energetic parameters are computed from a recently developed Vfold model for RNA secondary structure and pseudoknot folding thermodynamics. The folding kinetics theory is based on the complete conformational ensemble, including all the native-like and non-native states. The predicted folding and unfolding pathways, activation barriers, Arrhenius plots, and rate-limiting steps lead to several findings. First, for the PK5 pseudoknot, a misfolded 5' hairpin emerges as a stable kinetic trap in the folding process, and the detrapping from this misfolded state is the rate-limiting step for the overall folding process. The calculated rate constant and activation barrier agree well with the experimental data. Second, as an application of the model, we investigate the kinetic folding pathways for human telomerase RNA (hTR) pseudoknot. The predicted folding and unfolding pathways not only support the proposed role of conformational switch between hairpin and pseudoknot in hTR activity, but also reveal molecular mechanism for the conformational switch. Furthermore, for an experimentally studied hTR mutation, whose hairpin intermediate is destabilized, the model predicts a long-lived transient hairpin structure, and the switch between the transient hairpin intermediate and the native pseudoknot may be responsible for the observed hTR activity. Such finding would help resolve the apparent contradiction between the observed hTR activity and the absence of a stable hairpin.     

RNA pseudoknots downstream of the frameshift sites of retroviruses.

RNA pseudoknot structural motifs could have implications for a wide range of biological processes of RNAs. In this study, the potential RNA pseudoknots just downstream from the known and suspected retroviral frame-shift sites were predicted in the Rous sarcoma virus, primate immunodeficiency viruses (HIV-1, HIV-2, and SIV), equine infectious anemia virus, visna virus, bovine leukemia virus, human T-cell leukemia virus (types I and II), mouse mammary tumor virus, Mason-Pfizer monkey virus, and simian SRV-1 type-D retrovirus. Also, the putative RNA pseudoknots were detected in the gag-pol overlaps of two retrotransposons of Drosophila, 17.6 and gypsy, and the mouse intracisternal A particle. For each sequence, the thermodynamic stability and statistical significance of the secondary structure involved in the predicted tertiary structure were assessed and compared. Our results show that the stem-loop structures in the pseudoknots are both thermodynamically highly stable and statistically significant relative to other such configurations that potentially occur in the gag-pol or gag-pro and pro-pol junction domains of these viruses (300 nucleotides upstream and downstream from the possible frameshift sites are included). Moreover, the structural features of the predicted pseudoknots following the frameshift site of pro-pol overlaps of the HTLV-1 and HTLV-2 retroviruses are structurally well conserved. The occurrence of eight compensatory base changes in the tertiary interaction of the two related sequences allow the conservation of their tertiary structures in spite of the sequence divergence. The results support the possible control mechanism for frameshifting proposed by Brierley et al. and Jacks et al.     

RNA folding: pseudoknots, loops and bulges

The three-dimensional structures adopted by RNA molecules are crucial to their biological functions. The nucleotides of an RNA molecule interact to form characteristic secondary-structure motifs. Tertiary interactions orient these secondary-structure elements with respect to each other to form the functional RNA. Here we describe the basic structural elements with special emphasis on a novel tertiary motif, the pseudoknot.     

Asymmetry in RNA pseudoknots: observation and theory

RNA can fold into a topological structure called a pseudoknot, composed of non-nested double-stranded stems connected by single-stranded loops. Our examination of the PseudoBase database of pseudoknotted RNA structures reveals asymmetries in the stem and loop lengths and provocative composition differences between the loops. By taking into account differences between major and minor grooves of the RNA double helix, we explain much of the asymmetry with a simple polymer physics model and statistical mechanical theory, with only one adjustable parameter.     

PseudoViewer: automatic visualization of RNA pseudoknots

MOTIVATION: Several algorithms have been developed for drawing RNA secondary structures, however none of these can be used to draw RNA pseudoknot structures. In the sense of graph theory, a drawing of RNA secondary structures is a tree, whereas a drawing of RNA pseudoknots is a graph with inner cycles within a pseudoknot as well as possible outer cycles formed between a pseudoknot and other structural elements. Thus, RNA pseudoknots are more difficult to visualize than RNA secondary structures. Since no automatic method for drawing RNA pseudoknots exists, visualizing RNA pseudoknots relies on significant amount of manual work and does not yield satisfactory results. The task of visualizing RNA pseudoknots by hand becomes more challenging as the size and complexity of the RNA pseudoknots increase. RESULTS: We have developed a new representation and an algorithm for drawing H-type pseudoknots with RNA secondary structures. Compared to existing representations of H-type pseudoknots, the new representation ensures uniform and clear drawings with no edge crossing for any H-type pseudoknots. To the best of our knowledge, this is the first algorithm for automatically drawing RNA pseudoknots with RNA secondary structures. The algorithm has been implemented in a Java program, which can be executed on any computing system. Experimental results demonstrate that the algorithm generates an aesthetically pleasing drawing of all H-type pseudoknots. The results have also shown that the drawing has high readability, enabling the user to quickly and easily recognize the whole RNA structure as well as the pseudoknots themselves.     

PseudoBase: a database with RNA pseudoknots

PseudoBase is a database containing structural, functional and sequence data related to RNA pseudo-knots. It can be reached at http://wwwbio.Leiden Univ.nl/ approximately Batenburg/PKB.html. This page will direct the user to a retrieval page from where a particular pseudoknot can be chosen, or to a submission page which enables the user to add pseudoknot information to the database or to an informative page that elaborates on the various aspects of the database. For each pseudoknot, 12 items are stored, e.g. the nucleotides of the region that contains the pseudoknot, the stem positions of the pseudoknot, the EMBL accession number of the sequence that contains this pseudoknot and the support that can be given regarding the reliability of the pseudoknot. Access is via a small number of steps, using 16 different categories. The development process was done by applying the evolutionary methodology for software development rather than by applying the methodology of the classical waterfall model or the more modern spiral model.     

PseudoBase: structural information on RNA pseudoknots

PseudoBase is a database containing structural, functional and sequence data related to RNA pseudo-knots. It can be reached at http://wwwbio.LeidenUniv.nl/ approximately Batenburg/PKB.html. For each pseudoknot, thirteen items are stored, for example the relevant sequence, the stem positions of the pseudoknot, the EMBL accession number of the sequence and the support that can be given regarding the reliability of the pseudo-knot. Since the last publication, information on sizes of the stems and the loops in the pseudoknots has been added. Also added are alternative entries that produce surveys of where the pseudoknots are, sorted according to stem size or loop size.     

Identifying complete RNA structural ensembles including pseudoknots

The close relationship between RNA structure and function underlines the significance of accurately predicting RNA structures from sequence information. Structural topologies such as pseudoknots are of particular interest due to their ubiquity and direct involvement in RNA function, but identifying pseudoknots is a computationally challenging problem and existing heuristic approaches usually perform poorly for RNA sequences of even a few hundred bases. We survey the performance of pseudoknot prediction methods on a data set of full-length RNA sequences representing varied sequence lengths, and biological RNA classes such as RNase P RNA, Group I Intron, tmRNA and tRNA. Pseudoknot prediction methods are compared with minimum free energy and suboptimal secondary structure prediction methods in terms of correct base-pairs, stems and pseudoknots and we find that the ensemble of suboptimal structure predictions succeeds in identifying correct structural elements in RNA that are usually missed in MFE and pseudoknot predictions. We propose a strategy to identify a comprehensive set of non-redundant stems in the suboptimal structure space of a RNA molecule by applying heuristics that reduce the structural redundancy of the predicted suboptimal structures by merging slightly varying stems that are predicted to form in local sequence regions. This reduced-redundancy set of structural elements consistently outperforms more specialized approaches.in data sets. Thus, the suboptimal folding space can be used to represent the structural diversity of an RNA molecule more comprehensively than optimal structure prediction approaches alone.     

Characterization of the mechanical unfolding of RNA pseudoknots

The pseudoknot is an important RNA structural element that provides an excellent model system for studying the contributions of tertiary interactions to RNA stability and to folding kinetics. RNA pseudoknots are also of interest because of their key role in the control of ribosomal frameshifting by viral RNAs. Their mechanical properties are directly relevant to their unfolding by ribosomes during translation. We have used optical tweezers to study the kinetics and thermodynamics of mechanical unfolding and refolding of single RNA molecules. Here we describe the unfolding of the frameshifting pseudoknot from infectious bronchitis virus (IBV), three constituent hairpins, and three mutants of the IBV pseudoknot. All four pseudoknots cause −1 programmed ribosomal frameshifting. We have measured the free energies and rates of mechanical unfolding and refolding of the four frameshifting pseudoknots. Our results show that the IBV pseudoknot requires a higher force than its corresponding hairpins to unfold. Furthermore, its rate of unfolding changes little with increasing force, in contrast with the rate of hairpin unfolding. The presence of Mg²⁺ significantly increases the kinetic barriers to unfolding the IBV pseudoknot, but has only a minor effect on the hairpin unfolding. The greater mechanical stability of pseudoknots compared to hairpins, and their kinetic insensitivity to force supports the hypothesis that −1 frameshifting depends on the difficulty of unfolding the mRNA.     

Prediction of consensus RNA secondary structures including pseudoknots

Most functional RNA molecules have characteristic structures that are highly conserved in evolution. Many of them contain pseudoknots. Here, we present a method for computing the consensus structures including pseudoknots based on alignments of a few sequences. The algorithm combines thermodynamic and covariation information to assign scores to all possible base pairs, the base pairs are chosen with the help of the maximum weighted matching algorithm. We applied our algorithm to a number of different types of RNA known to contain pseudoknots. All pseudoknots were predicted correctly and more than 85 percent of the base pairs were identified.     

Apical loop-internal loop RNA pseudoknots: a new type of stimulator of -1 translational frameshifting in bacteria

Nearly all members of a widespread family of bacterial transposable elements related to insertion sequence 3 (IS3), therefore called the IS3 family, very likely use programmed -1 ribosomal frameshifting to produce their transposase, a protein required for mobility. Comparative analysis of the potential frameshift signals in this family suggested that most of the insertion sequences from the IS51 group contain in their mRNA an elaborate pseudoknot that could act as a recoding stimulator. It results from a specific intramolecular interaction between an apical loop and an internal loop from two stem-loop structures. Directed mutagenesis, chemical probing, and gel mobility assays of the frameshift region of one element from the IS51 group, IS3411, provided clear evidences of the existence of the predicted structure. Modeling was used to generate a three-dimensional molecular representation of the apical loop-internal loop complex. We could demonstrate that mutations affecting the stability of the structure reduce both frameshifting and transposition, thus establishing the biological importance of this new type of RNA structure for the control of transposition level.     

A heuristic approach for detecting RNA H-type pseudoknots

MOTIVATION: RNA H-type pseudoknots are ubiquitous pseudoknots that are found in almost all classes of RNA and thought to play very important roles in a variety of biological processes. Detection of these RNA H-type pseudoknots can improve our understanding of RNA structures and their associated functions. However, the currently existing programs for detecting such RNA H-type pseudoknots are still time consuming and sometimes even ineffective. Therefore, efficient and effective tools for detecting the RNA H-type pseudoknots are needed. RESULTS: In this paper, we have adopted a heuristic approach to develop a novel tool, called HPknotter, for efficiently and accurately detecting H-type pseudoknots in an RNA sequence. In addition, we have demonstrated the applicability and effectiveness of HPknotter by testing on some sequences with known H-type pseudoknots. Our approach can be easily extended and applied to other classes of more general pseudoknots. AVAILABILITY: The web server of our HPknotter is available for online analysis at http://bioalgorithm.life.nctu.edu.tw/HPKNOTTER/ CONTACT: cllu@mail.nctu.edu.tw, chiu@cc.nctu.edu.tw     

Predicting RNA secondary structures with pseudoknots by MCMC sampling

The most probable secondary structure of an RNA molecule, given the nucleotide sequence, can be computed efficiently if a stochastic context-free grammar (SCFG) is used as the prior distribution of the secondary structure. The structures of some RNA molecules contain so-called pseudoknots. Allowing all possible configurations of pseudoknots is not compatible with context-free grammar models and makes the search for an optimal secondary structure NP-complete. We suggest a probabilistic model for RNA secondary structures with pseudoknots and present a Markov-chain Monte-Carlo Method for sampling RNA structures according to their posterior distribution for a given sequence. We favor Bayesian sampling over optimization methods in this context, because it makes the uncertainty of RNA structure predictions assessable. We demonstrate the benefit of our method in examples with tmRNA and also with simulated data. McQFold, an implementation of our method, is freely available from http://www.cs.uni-frankfurt.de/~metzler/McQFold.     

RNA aptamers that bind the nucleocapsid protein contain pseudoknots

We screened two independent RNA libraries consisting of molecules of 50 nucleotides of random sequence, one of which had additional viral psi-sequences to isolate RNA aptamers that bound to the mature form of the nucleocapsid (NC) protein of Human Immunodeficiency Virus Type-1 (HIV-1). Surface Plasmon Resonance measurements and gel shift assays showed that the RNA aptamers bound with high affinity and specificity. We employed RNase footprinting to characterize the RNA structures and to map their protein binding sites. Most of the selected RNA aptamers contained a plausible pseudoknot in addition to the characteristic stem-loop structure. Moreover, the pseudoknots were part of the NC binding sites. We propose that higher order structures such as pseudoknots may constitute binding motifs for nucleic acid binding proteins, especially for NC protein, which is a nucleic acid chaperone.     

Viral RNA pseudoknots: versatile motifs in gene expression and replication

RNA pseudoknots are structural elements found in almost all classes of RNA. First recognized in the genomes of plant viruses, they are now established as a widespread motif with diverse functions in various biological processes. This Review focuses on viral pseudoknots and their role in virus gene expression and genome replication. Although emphasis is placed on those well defined pseudoknots that are involved in unusual mechanisms of viral translational initiation and elongation, the broader roles of pseudoknots are also discussed, including comparisons with relevant cellular counterparts. The relationship between RNA pseudoknot structure and function is also addressed.     

An RNA folding method capable of identifying pseudoknots and base triples

MOTIVATION: Recently, we described a Maximum Weighted Matching (MWM) method for RNA structure prediction. The MWM method is capable of detecting pseudoknots and other tertiary base-pairing interactions in a computationally efficient manner (Cary and Stormo, Proceedings of the Third International Conference on Intelligent Systems for Molecular Biology, pp. 75-80, 1995). Here we report on the results of our efforts to improve the MWM method's predictive accuracy, and show how the method can be extended to detect base interactions formerly inaccessible to automated RNA modeling techniques. RESULTS: Improved performance in MWM structure prediction was achieved in two ways. First, new ways of calculating base pair likelihoods have been developed. These allow experimental data and combined statistical and thermodynamic information to be used by the program. Second, accuracy was improved by developing techniques for filtering out spurious base pairs predicted by the MWM program. We also demonstrate here a means by which the MWM folding method may be used to detect the presence of base triples in RNAs. AVAILABILITY: http://www.cshl.org/mzhanglab/tabaska/j axpage. html CONTACT: tabaska@cshl.org